Ultrafine nanoporous intermetallic catalysts by high-temperature liquid metal dealloying for electrochemical hydrogen production

Intermetallic compounds formed from non-precious transition metals are promising cost-effective and robust catalysts for electrochemical hydrogen production. However, the development of monolithic nanoporous intermetallics, with ample active sites and sufficient electrocatalytic activity, remains a challenge. Here we report the fabrication of nanoporous Co7Mo6 and Fe7Mo6 intermetallic compounds via liquid metal dealloying. Along with the development of three-dimensional bicontinuous open porosity, high-temperature dealloying overcomes the kinetic energy barrier, enabling the direct formation of chemically ordered intermetallic phases. Unprecedented small characteristic lengths are observed for the nanoporous intermetallic compounds, resulting from an intermetallic effect whereby the chemical ordering during nanopore formation lowers surface diffusivity and significantly suppresses the thermal coarsening of dealloyed nanostructure. The resulting ultrafine nanoporous Co7Mo6 exhibits high catalytic activity and durability in electrochemical hydrogen evolution reactions. This study sheds light on the previously unexplored intermetallic effect in dealloying and facilitates the development of advanced intermetallic catalysts for energy applications.

Intermetallic compounds formed from non-precious transition metals are promising cost-effective and robust catalysts for electrochemical hydrogen production. However, the development of monolithic nanoporous intermetallics, with ample active sites and sufficient electrocatalytic activity, remains a challenge. Here we report the fabrication of nanoporous Co 7 Mo 6 and Fe 7 Mo 6 intermetallic compounds via liquid metal dealloying. Along with the development of three-dimensional bicontinuous open porosity, hightemperature dealloying overcomes the kinetic energy barrier, enabling the direct formation of chemically ordered intermetallic phases. Unprecedented small characteristic lengths are observed for the nanoporous intermetallic compounds, resulting from an intermetallic effect whereby the chemical ordering during nanopore formation lowers surface diffusivity and significantly suppresses the thermal coarsening of dealloyed nanostructure. The resulting ultrafine nanoporous Co 7 Mo 6 exhibits high catalytic activity and durability in electrochemical hydrogen evolution reactions. This study sheds light on the previously unexplored intermetallic effect in dealloying and facilitates the development of advanced intermetallic catalysts for energy applications.
Electrochemical hydrogen production through water splitting has emerged as a promising strategy for the effective utilization and storage of intermittent renewable energy. Crucial to this technology is the realization of high-efficiency electrocatalytic hydrogen evolution reactions (HERs), particularly in alkaline media 1 . Pt and its alloys are currently the most active HER catalysts [2][3][4] . However, the scarcity and high cost of Pt limit their large-scale practical applications in electrolysers. Tremendous research efforts have been devoted to the development of low-cost, yet efficient, electrocatalysts based on earthabundant transition metals, as alternatives to noble Pt, for HERs [5][6][7] . Monometallic transition metals (Fe, Co, Ni, Ti, W, Mo, Cu, etc.) show moderate catalytic activity, while alloys of these elements can substantially improve HER catalysis by modifying both active site morphology (geometric effect) [8][9][10] and electronic structure (electronic effect) [11][12][13] to generate desirable catalytic transition states with minimum energy barriers. Compared to random solid-solution alloys, intermetallic compounds with ordered atomic structures and welldefined stoichiometry possess the merits of homogeneous and intensified active sites as well as the capability to form unique crystal structures not commonly demonstrated by random solid-solutions to enhance the geometry effect 10,14,15 . The combination of electron localization and directional covalent bonding in intermetallic catalysts can also strengthen the electronic effect 14 . Moreover, the strong ionic/ covalent interactions between the metal constituents are expected to enhance the chemical/electrochemical stability of intermetallic catalysts during catalytic processes. Intermetallic compounds, such as Ni 4 Mo 16 , Co 3 Mo 10 , NiZn 17 , and Ni 3 Al 18 , are active HER electrocatalysts with appreciable energy efficiencies. Apart from the selection of intermetallic compounds with high intrinsic HER activity, a large specific surface area facilitating reactant adsorption, reaction, and desorption is essential for effectively utilizing the high catalytic activity of an intermetallic catalyst. In addition to the extensively studied particulate catalysts, bicontinuous porous nanostructures, with large surface areas, open pore channels, and high electrical conductivities, effectively maximize the density and accessibility of active sites and have emerged as a new type of electrocatalyst [19][20][21][22][23][24] . Three-dimensional (3D) bicontinuous nanoporous structures fabricated by dealloying 25 , the selective removal of the less stable component(s) from an alloy, are very attractive owing to their large specific surface area with ample surface defects, high electric conductivity, and rapid mass transport pathways 19,26 . Several intermetallic compounds have been fabricated or integrated into 3D porous structures by the chemical etching of heterogeneous precursors (such as Mg 2 Cu 27 , PtSi 28 , (Pt 1-x M x ) 3 Al (M = Ni, Co, Fe) 29-31 , SbSn 32 , and Pd 3 Bi 24 ) or by segregation as nanoparticulate phases anchored on 3D nanoporous metal frameworks during dealloying (such as Cu 3 Sn/Cu 33 , Co 3 Mo/Cu 10 , Al 7 Cu 4 Ni/Cu 34 , and Nb 5 Si 3 /NbTi 35 ). However, these porous intermetallic materials exhibit low flexibility in microstructural optimization, high electric resistance due to copious grain boundaries and interfaces, and poor mechanical stability. Although monolithic nanoporous intermetallic compounds with tunable bicontinuous nanoporosity are desirable for efficient electrocatalysis in energy-related reactions, fabricating bicontinuous nanoporous intermetallic catalysts from single-phase precursors remains a challenge because of the difficulty in forming chemically ordered intermetallic phases during low-temperature chemical dealloying. Accordingly, advanced HER electrocatalysts, based on non-noble nanoporous intermetallics with sufficiently high HER activity and robustness, are yet to be developed.
In this work, we report a liquid metal dealloying (LMD) strategy, conducted at elevated temperatures, to fabricate 3D nanoporous Mobased intermetallic compounds as high-performance HER electrocatalysts. Coupled with the simultaneous evolution of 3D bicontinuous open porosity during the dealloying of single-phase precursors, the high-temperature LMD process overcomes the energy barrier, driving the direct formation of chemically ordered intermetallic phases. Beyond the conventional wisdom that porous metals produced by LMD typically have large feature sizes and therefore small specific surface areas for catalytic applications, here, the intermetallic Co 7 Mo 6 and Fe 7 Mo 6 exhibit fine nanoporous structures with ligaments/pores that are~30 nm in size. Combined experimental analyses and molecular dynamics simulations uncovered an intermetallic effect, whereby high-temperature chemical ordering during nanopore formation suppresses dealloyed-nanostructure coarsening. The ultrafine 3D nanoporous μ-Co 7 Mo 6 , with a large accessible surface area and abundant active sites, exhibits high HER catalysis in 1 M KOH alkaline electrolyte.

Results and discussion
Design, fabrication, and structural characterization LMD is a processing technique utilizing the difference in the miscibility of alloy components in a molten metal bath to corrode selected component(s) while retaining the others, self-organizing into a 3D porous structure [36][37][38][39] . According to the design principle (Fig. 1a), in the precursor alloy (AB), the pore-forming metal (A) and sacrificial component (B) should have a positive and negative enthalpy of mixing with the melt bath (C), respectively. LMD systems were designed accordingly to fabricate nanoporous Mo-based intermetallic compounds. A mixture of Mo with Co, Fe, or Cr, with designated compositions, was used as the pore-forming component A, while Ni and Mg were chosen as the sacrificial component B and melt bath C, respectively 36,37 . As shown in Fig. 1b, Mo, Fe, Cr, and Co have a positive enthalpy of mixing with Mg, whereas the enthalpy of mixing is negative between Ni and Mg, satisfying the principle of LMD 40 30 were also prepared for fabricating nanoporous Mo and Fe, as references. All the precursors are single-phase face-centered cubic (fcc) alloys, as verified by X-ray diffraction (XRD) (Supplementary Fig. 1).
The Ni 70 (Co 0.55 Mo 0.45 ) 30 system is used as an example to depict the fabrication of nanoporous intermetallic compounds via LMD. LMD was carried out by immersing a 200 μm-thick Ni 70 (Co 0.55 Mo 0.45 ) 30 sheet sample into a 973 K Mg melt. During this process, Ni selectively dissolved into Mg, and Co-Mo spontaneously evolved into a bicontinuous porous solid structure at the alloy/melt interface. Owing to the fast dealloying velocity (in the order of 5-10 μm s −1 ) 39,41 , dealloying was completed in a short time (120 s). After cooling, the Mg melt was frozen in the porous structure, which was subsequently etched away using a dilute acid to expose the Co-Mo open porous structure. The changes of macroscopic morphology, phase, and microstructure are traced using optical photographs, XRD and scanning electron microscopy (SEM) images as shown in Fig. 1c-g, respectively. The fcc precursor Ni 70 (Co 0.55 Mo 0.45 ) 30 exhibits an average grain size of~15 μm and a uniform distribution of Ni, Co, and Mo ( Fig. 1e and Supplementary  Fig. 2). Significantly, the intermetallic compound μ-Co 7 Mo 6 (JCPDS 29-0489) together with the solidified Mg phase (JCPDS 35-0821) can be detected after LMD (Fig. 1d). The corresponding SEM image shows a bicontinuous nanocomposite consisting of interconnected μ-Co 7 Mo 6 (bright contrast) and Mg (dark contrast) phases, which are the characteristic of nanoporous structures generated by dealloying (Fig. 1f). The feature/ligament size is measured to be 30.8 nm, using the Fiji package of the ImageJ software ( Supplementary Fig. 3) 42 . After Mg removal, nanoporous μ-Co 7 Mo 6 with a well-maintained bicontinuous structure is obtained (Fig. 1g). In agreement with the nanoscale ligament/pore size, the XRD pattern of nanoporous μ-Co 7 Mo 6 shows broad diffraction peaks (Fig. 1d). Notably, the final nanoporous μ-Co 7 Mo 6 inherits the free-standing sheet morphology of the precursor alloy with a well-preserved 2 cm × 1 cm lateral dimension ( Fig. 1c and Supplementary Fig. 4). Due to LMD-induced volume contraction, the thickness of the sheet decreases from 200 μm to 170 μm. The nanoporous μ-Co 7 Mo 6 is further characterized by transmission electron microscopy (TEM). The bright-field TEM image shows interconnected ligaments composed of crystallites of~30 nm in size (Fig. 1h). Intriguingly, this polycrystalline structure with nanosized grain ligaments is distinct from the typical microstructure of nanoporous gold dealloyed from Au-Ag alloys, which often retains the original grain structure of parent alloys 43,44 . Such distinction is likely owing to the difference in dealloyed phase formation between two alloy systems. The Au-Ag alloy system can form an ideal solid solution and has very small difference in atomic volumes between Au and Ag, allowing for an essentially coherent transformation from parent alloy to nanoporous product structure. In contrast, the LMD of nanoporous μ-Co 7 Mo 6 is fulfilled by the phase transformation from fcc-Ni 70 (Co 0.55 Mo 0.45 ) 30 to trigonal μ-Co 7 Mo 6 with distinctly different crystal structures and lattice parameters (Supplementary Table 2). Consequently, the development of μ-Co 7 Mo 6 ligaments during the dealloying of fcc-Ni 70 (Co 0.55 Mo 0.45 ) 30 cannot be coherent and epitaxial, but is more likely through an interfacial heterogeneous nucleation and growth process, resulting in the formation of polycrystalline ligaments with nanosized grains. Similar polycrystalline structures had been observed in nanoporous gold produced by chemical dealloying of amorphous Au 40 Cu 28 Ag 7 Pd 5 Si 20 alloy 45 , nanoporous Si by LMD of Mg 2 Si alloy 46 , and nanoporous Ni by vapor phase dealloying of Ni 2 Zn 11 alloy 47 . Despite being polycrystalline and inherently brittle, the nanoporous μ-Co 7 Mo 6 maintains structural integrity and is mechanically robust due to the interconnections of ligaments in 3D space (Fig. 1c, Supplementary Figs. 4 and 5). The chemical composition of nanoporous μ-Co 7 Mo 6 is verified by energydispersive X-ray spectroscopy (EDX) mappings, showing the uniform distribution of Co and Mo in the ligaments (Fig. 1h), which is in accordance with the observation of single-phase, as detected by XRD. Figure 1i and j show the atomic-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of nanoporous μ-Co 7 Mo 6 and the corresponding fast Fourier transform (FFT) pattern, respectively. The clear lattice fringes with d-spacings of 0.24 and 0.21 nm, highlighted in Fig. 1i, correspond to the (11 20) and (000 12) crystal planes of the trigonal μ-Co 7 Mo 6 (space group 166, R-3m) 48 . The X-ray photoelectron spectroscopy (XPS) spectra collected from the surfaces of nanoporous μ-Co 7 Mo 6 show predominantly metallic Co and Mo signals along with some signals corresponding to oxidized Mo 4+ , Mo 5+ , Mo 6+ , and Co 2+ species, most likely formed by air-exposure ( Supplementary Fig. 6). According to the Pourbaix diagrams of Mo and Co 49,50 , these oxidized species can be reduced to metallic states during electrolysis on reduction polarization.
The microstructural characterizations confirmed the formation of monolithic 3D nanoporous structure for the intermetallic compound μ-Co 7 Mo 6 . This is the first report of the direct fabrication of a nanoporous intermetallic compound by LMD, via atomic selfassembly at the alloy/melt dealloying fronts. As a reference, it is found that the Ni 70 (Co 0.55 Mo 0.45 ) 30 alloy cannot be dealloyed chemically in 0.5 M H 2 SO 4 , HCl, or HNO 3 solutions at room temperature ( Supplementary Fig. 7), due to the low ambient-temperature surface-diffusivity of Mo and surface passivation after leaching the top few atomic layers 51 . Therefore, the LMD is of vital importance in fabricating nanoporous intermetallic compounds, owing to the elevated dealloying temperatures that accelerate atomic diffusivity for successful dealloying and drive the formation of chemical order for the intermetallic phases.

The intermetallic effect on LMD
The thermal coarsening of dealloyed nanoporous materials is a surface diffusion-controlled process 54,55 . Sieradzki et al. 51 proposed an empirical correlation describing the scaling relation between the ligament size and inverse homologous temperature, 1/T H = T m /T dealloy , where T m is the melting point of the pore-forming components (metals and alloys), and T dealloy is the dealloying temperature, as shown in Fig. 3a. A survey of the literature data indicates a general trend that electrochemical dealloying (ECD) occupies the high 1/T H region, with ligament sizes mostly below 100 nm, while high-temperature LMD corresponds to the low 1/T H region, with ligaments of hundreds of nanometer in size 39,56 . The scaling correlation between the ligament size and 1/T H applies to both ECD and LMD. Plotting our LMD results at various temperatures in this diagram ( Fig. 3a and Supplementary Figs. 10-14), a reasonable fit of the data to the conventional trend for nanoporous pure metals bcc-Mo, bcc-Fe, and solid-solution bcc-Cr 50 Mo 50 is observed, even though their ligament sizes are relatively smaller than the literature data because of the different dealloying times (120 s for this study and 10-20 min in the literature). Significantly, a distinct deviation from the conventional scaling relation is observed for nanoporous intermetallic compounds of both μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 ( Fig. 3a). To eliminate the effect of the dealloying time, nanoporous μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 were also fabricated with 15 min of dealloying time (Supplementary Figs. 10 and 11). As shown in Fig. 3a (as the open symbols), the ligament/pore sizes remain small and continue to deviate significantly from the typical scaling relationship. This indicates a unique and previously unexplored effect of intermetallic compounds in hindering the thermal coarsening of dealloyed nanoporous structures at high temperatures. Note that although the formation of surface oxides could also suppress surface diffusion 57 , this effect could be excluded here as the LMD and pore formation are conducted in a highly reducing molten Mg environment. In contrast to pure metals and solid-solution alloys, μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 intermetallic compounds have chemically ordered crystal structures with covalent bonding, rather than pure metallic bonding 58,59 . The μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 have topologically closepacked (TCP) structures, with alternating Zr 4 Al 3 and MgCu 2 -type layers 48,52 (Supplementary Fig. 15). Such an ordered lattice structure, with solely tetrahedral interstices 60 , renders much slower atomic mobility than simple fcc or bcc metals. Additionally, covalent bonding with a high bond energy makes it difficult for atoms to hop 52,58,59 , forming another barrier for atomic diffusion. The suppressed atomic diffusivity of the intermetallic compounds is confirmed by molecular dynamics simulations. The 14 nm × 15 nm × 8 nm models were built by sandwiching an 8 nm-thick slat of μ-Co 7 Mo 6 ,  10) and (0001) for hcp-Co), between two 3 nm-thick molten Mg layers (Fig. 3c-e). The models were relaxed in the 900-1200 K temperature range, and the mean square displacement over a duration of 20 ns was calculated for the three atomic layers at the metal/Mg melt interfaces to derive interfacial diffusivity, according to the Einstein-Smoluchowski relation 61 (Supplementary Fig. 16). The obtained average diffusivities are plotted against 1/T H , as shown in Fig. 3b. The surface diffusivities of bcc-Mo, hcp-Co, and Co in μ-Co 7 Mo 6 follow a unified linear trend, but Mo in μ-Co 7 Mo 6 shows an apparent downward variation. Considering that the ligament size (d(t)) is related to surface diffusivity (D s ) according to dðtÞ n = KtD s (where K is a constant; t is the dealloying time; and n, approximately 4, is the coarsening exponent) 47,62,63 , the result is in good agreement with the trend of ligament size versus 1/T H , as shown in Fig. 3a. Therefore, the ultrafine pore/ligament sizes of the nanoporous intermetallic compounds originate from suppressed Mo atomic diffusivity, particularly at the surfaces and interfaces of the intermetallic compounds. Based on the calculated diffusivities, activation energies of surface diffusion are determined to be 59.8, 84.2, 84.7, and 102.5 kJ mol −1 for hcp-Co, bcc-Mo, Co in μ-Co 7 Mo 6 , and Mo in μ-Co 7 Mo 6 , respectively (Supplementary Table 3). Therefore, the intermetallic phase provides a large energy barrier for the surface diffusion of Co and Mo atoms.

Mechanisms for the evolution of ultrafine nanoporous intermetallic compounds
Based on the above experimental analyses and molecular dynamics simulations, a scheme for fabricating ultrafine nanoporous intermetallic compounds by LMD is outlined in Fig. 4. Taking nanoporous μ-Co 7 Mo 6 as an example, immersing the single-phase Ni 70 (Co 0.55 Mo 0.45 ) 30 alloy into the Mg melt selectively dissolves the Ni atoms, leaving behind Co and Mo atoms at the alloy/melt interfaces, which diffuse and self-assemble into a 3D nanoporous solid structure. Despite the thermodynamic advantages, the formation of an ordered intermetallic phase is kinetically hampered by a high energy barrier 14 . The LMD overcomes this energy barrier by virtue of its high temperatures, enabling the concurrent formation of the chemically ordered μ-Co 7 Mo 6 phase and bicontinuous nanoporosity, which facilitate the direct formation of nanoporous intermetallic compounds. In the dealloying process, nanopore formation is followed by thermal coarsening, which is a surface-diffusion-controlled process driven by thermodynamic surface-energy reduction 39,64,65 .
For conventional metals and random solid-solution alloys with moderate energy barriers of surface diffusion, high-temperature LMD drives severe thermal coarsening because of the significantly accelerated surface diffusivity, forming very coarse porous structures with pore/ligament sizes larger than hundreds of nanometer. In contrast, intermetallic compounds have a much larger energy barrier for surface diffusion, which regulates slow surface diffusivity even under high-temperature LMD conditions, significantly suppressing dealloyed-nanostructure coarsening and forming nanoporous intermetallic compounds with an ultrafine feature size. In the typical low 1/T H region of LMD, nanoporous μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 show very small ligament sizes of 20-100 nm, which are up to two orders of magnitude smaller than those of conventional nanoporous metals processed by LMD (Fig. 3a). Therefore, the intermetallic effect enables the utilization of high-temperature LMD for orderedintermetallic-phase formation, while maintaining a fine nanoporous structure by circumventing the severe thermal coarsening. This is particularly advantageous for fabricating 3D nanoporous intermetallic compounds for electrocatalytic reactions, as fine structures with large surface areas and abundant under-coordinated surface defects contribute to high catalytic activity 66,67 .

Electrochemical characterizations
The electrocatalytic performance of the nanoporous intermetallic compounds for the HER was evaluated in a 1 M KOH aqueous solution at room temperature. Two forms of the intermetallic catalysts were investigated: powder samples and self-supported monolithic sheets. The powder samples were prepared from as-dealloyed nanoporous sheets by mechanical grinding and high-power ultrasonication (Supplementary Fig. 17). As a mixture with conductive carbon and nafion binder, they were cast onto a glassy carbon disk electrode to make thin films with a 2 mg cm −2 catalyst loading. Such thin film electrodes can reduce the ion diffusion constraints that thick nanoporous sheet electrodes may suffer, allowing for a more precise assessment of the intrinsic activity of nanoporous electrocatalysts. Figure 5a-d illustrate the electrochemical HER performance of nanoporous Mo-based intermetallic compounds and the reference materials. All nanoporous catalysts were fabricated at the temperature of 973 K. Based on the multiple criteria of onset potential (Fig. 5a), Tafel slope (Fig. 5b, c), operating potential at 10 mA cm −2 geo current density (Fig. 5a, c), and charge transfer resistance (R ct ) from electrochemical impedance spectroscopy (EIS) measurements (Fig. 5d), the catalytic activities exhibit the following trend: Pt/C > μ-Co 7 Mo 6 > μ-Fe 7 Mo 6 > Mo > Cr 50 Mo 50 . Pure carbon is essentially inert in the tested potential range. Among the nanoporous electrocatalysts, μ-Co 7 Mo 6 demonstrats the lowest overpotential of 76 mV at 10 mA cm −2 geo current density, the lowest Tafel slope of 82 mV dec −1 , and the smallest R ct of 5.1 Ω, indicating the highest HER kinetics and catalytic efficiency. The catalytic activity of nanoporous μ-Co 7 Mo 6 is close, though yet inferior, to that of Pt/C.
To assess the intrinsic activity of the catalysts, the electrochemical surface areas (ECSAs) of the nanoporous electrocatalysts were calculated by measuring their double layer capacitances (C dl ) (Supplementary Fig. 18). The ECSAs for nanoporous μ-Co 7 Mo 6 , μ-Fe 7 Mo 6, Cr 50 Mo 50 , and Mo are determined to be 44.6, 54.9, 9.3, and 16.9 m 2 g −1 , respectively, clearly demonstrating an abundance of active sites in the fine-structured nanoporous intermetallic compounds. The ECSAnormalized HER polarization curves, in Supplementary Fig. 18h, indicate an intrinsic catalytic activity trend of the order of μ-Co 7 Mo 6 > Mo > Cr 50 Mo 50 > μ-Fe 7 Mo 6 . The activity trend for μ-Co 7 Mo 6 , Mo, and Cr 50 Mo 50 remains unchanged compared to the geometric-surface-area-normalized results. However, nanoporous μ-Fe 7 Mo 6 exhibits lower intrinsic activity but higher apparent activity (on a geometric surface area basis) than nanoporous Mo and Cr 50 Mo 50 , indicating that the large surface area and associated abundant active sites originating from a small ligament size of nanoporous μ-Fe 7 Mo 6 contribute to the enhanced catalytic performance. In contrast to μ-Fe 7 Mo 6 , the nanoporous μ-Co 7 Mo 6 has both the highest intrinsic activity and a fine porous structure for a large surface area, resulting in the highest catalytic activity among the nanoporous electrocatalysts. The superior HER activity of μ-Co 7 Mo 6 over μ-Fe 7 Mo 6 could be attributed to the electronic effect that the stronger d-electron  interactions between Co and Mo in this hypo-hyper-d-electronic combinations modulate the optimal adsorption/desorption of reaction intermediates 68,69 . The nanoporous μ-Co 7 Mo 6 fabricated by LMD at various temperatures were also examined as powder samples to determine the effect of pore/ligament size on the electrochemical properties. The three samples prepared at 873 K, 973 K, and 1073 K exhibit ligament diameters of 20.7, 30.8, and 43.1 nm, respectively (Supplementary Fig. 9 and Supplementary Table 4). As depicted in Fig. 5e and Supplementary Fig. 19, lower dealloying temperatures and smaller ligament sizes result in larger HER current densities on a geometric surface area basis for a given overpotential, indicating higher catalytic activity. The measured ECSAs for these electrocatalysts are 53.5, 44.6, and 24.1 m 2 g −1 , respectively (Supplementary Fig. 20). Remarkably, the ECSA-normalized HER polarization curves of the three electrocatalysts overlap when the current density is less than 0.037 mA cm −2 ECSA (equivalent to 40 mA cm −1 geo for the 873 K sample), suggesting that they all possess the same intrinsic catalytic activity (Fig. 5f). Therefore, the smaller-ligament-induced increment in apparent catalytic efficiency is due to a structural effect in which a larger specific surface area provides a larger number of catalytically active sites for electrochemical reactions. This structural effect highlights the significance of the intermetallic effect in realizing the nanoscale porosity structure of Mo-based intermetallic compounds for superior electrochemical performance. Note that when the current density exceeds 40 mA cm −1 geo , the 873 K sample's activity decreases and becomes lower than that of the 973 K sample (Fig. 5e, f). This is probable because the ultrafine porous structure (20.7 nm pore size) of the 873 K sample limits ion/gas transport at high current densities 70 . Under the current testing conditions, the 973 K sample with a pore size of 30.8 nm appears to be the optimal electrocatalyst capable of balancing the intrinsic reaction kinetics and accessibility of active sites.
The monolithic nanoporous intermetallic compounds are mechanically robust and can therefore be used as self-supported HER electrodes. Figure 6a shows the HER polarization curve of nanoporous μ-Co 7 Mo 6 sheet electrodes with a dimension of 1 cm × 0.5 cm × 170 μm ( Supplementary Fig. 21), in comparison to a Pt/C electrode drop-cast on carbon paper with a similarly high catalyst loading of 24.4 mg cm −2 . Due to intensified active sites from the bulk electrode, the nanoporous μ-Co 7 Mo 6 sheet delivers improved HER performance compared to its powder counterpart, exhibiting a~0 V onset potential, a 46 mV dec −1 Tafel slope, and a 14 mV overpotential at 10 mA cm −2 geo current density Potential (V vs RHE) np-Co 7 Mo 6 @873 K np-Co 7 Mo 6 @973 K np-Co 7 Mo 6 @1073 K c Comparisons of overpotential at 10 mA cm −2 geo current density and Tafel slopes. d EIS spectra collected at 200 mV overpotential. The insets are the zoom-in spectra and the electronic circuit for EIS fitting. e, f iR-corrected HER polarization curves with current normalized by the geometric surface area and the electrochemical active surface area (ECSA), respectively, for np-Co 7 Mo 6 fabricated by LMD at the temperatures of 873 K, 973 K, and 1073 K. The catalyst loading is 2 mg cm −2 for all samples except for pure carbon.
Article https://doi.org/10.1038/s41467-022-32768-1 (Fig. 6a, b and Supplementary Fig. 22). The property is among the best performances reported for non-precious Mo-based HER electrocatalysts ( Fig. 6c and Supplementary Table 5). Due to the inferior intrinsic activity of nanoporous μ-Co 7 Mo 6 compared to that of Pt/C, the μ-Co 7 Mo 6 sheet exhibits larger overpotentials at current densities below 55 mA cm −2 geo than Pt/C (Fig. 6a). In contrast, μ-Co 7 Mo 6 outperforms Pt/C at high current densities exceeding 55 mA cm −2 geo . For instance, an overpotential of 115 mV is required to obtain a current density of 150 mA cm −2 geo for nanoporous μ-Co 7 Mo 6 , which is significantly lower than the 180 mV necessary for Pt/C (Fig. 6b). While the low-current-density property of the electrocatalysts is mainly controlled by kinetics, at higher current densities the density and accessibility of active sites can dominate the performance, particularly in the porous electrodes. Therefore, the comparison between nanoporous μ-Co 7 Mo 6 and Pt/C demonstrates that the 3D bicontinuous porous structure facilitates the electrochemical reactions of the intermetallic compounds by readily exposing more active sites, rendering the nanoporous μ-Co 7 Mo 6 particularly suitable for high-current applications. Moreover, unlike Pt/C electrodes, which are prone to exfoliation due to the severe production of H 2 bubbles at high current densities, the robust self-supported μ-Co 7 Mo 6 sheet with 3D interconnected ligaments has a far better structural stability. Along with excellent electrocatalytic activity, the nanoporous μ-Co 7 Mo 6 electrodes exhibit excellent durability. After 5000 cycles of accelerated degradation testing by cyclic voltammetry, the nanoporous electrode shows a negligible shift in the HER polarization curves and negligible change in    its porous structure (Fig. 6d). Furthermore, the nanoporous μ-Co 7 Mo 6 delivers a high current density of~170 mA cm −2 at 150 mV overpotential, without significant current decay over a long-term chronoamperometry test for 48 h (Fig. 6e). It is necessary to note that despite the enhanced catalytic efficiency of self-supported nanoporous μ-Co 7 Mo 6 , the sheet electrodes have a much lower material utilization efficiency than powder samples ( Supplementary Fig. 23) because only the near surface layers of the thick electrodes may contribute to electrochemical reactions, particularly at a high current density. High material efficiency would necessitate further optimization of the sheet thickness and the nanoporous structure. In addition, advanced catalyst integration techniques must be developed in order to implement the intrinsically brittle nanoporous μ-Co 7 Mo 6 sheet as large-sized electrodes in commercial electrolyzers. By contrast, the powder form of the nanoporous intermetallic electrocatalysts, which can be spray-coated on substrates to make scalable electrodes with high material efficiency 71 , might be readily applicable for practical hydrogen production applications. In summary, we presented a high-temperature LMD strategy for fabricating 3D nanoporous intermetallic catalysts of μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 . The formation of pore-forming intermetallic compounds leads to slow atomic diffusivity and retards thermal coarsening of nanoporous structures at high temperatures. The characteristic ligament sizes of nanoporous μ-Co 7 Mo 6 and μ-Fe 7 Mo 6 are only tens of nanometer, notably departing from the conventional scaling relationship between the ligament size and dealloying temperature. The nanoporous μ-Co 7 Mo 6 with ultrafine porous structure exhibits high electrocatalytic activity and durability, indicating its potential use as a commercial HER catalyst for high-current applications. This study sheds light on the intermetallic effect on tailoring nanostructures of dealloyed materials and could assist the development of advanced nanoporous intermetallic electrocatalysts for a broad range of energy applications. (atomic ratios) were prepared from pure metals (Ni (99.9%) from FUJIFILM Wako Pure Chemical Co., Osaka, Japan; Co (99.99%) from Rare Metallic Co., Ltd., Tokyo, Japan; Fe (>99.95%) from Toho Zinc Co., Ltd., Tokyo, Japan; Cr (99.9%) from Kojundo Chemical Laboratory Co., Ltd., Saitama, Japan; Mo (99.95%) from Furuuchi Chemical Co., Tokyo, Japan) by arc melting in the argon atmosphere. The as-prepared ingots were re-melted in a tilt casting machine with argon protection and casted into thick plates with a thickness of 5 mm. The plates were further cold rolled into a thickness of 200 μm and then thermally treated at 1273 K for 8 h for homogenization and relieving the internal stress. The liquid metal dealloying (LMD) was carried out in a helium atmosphere using a magnesium melt (Mg (99.9%) from Rare Metallic Co., Ltd., Tokyo, Japan). The magnesium was melted and heated to temperatures of 973 K, 1073 K, or 1173 K by induction heating. The precursor alloy sheets of Ni 70

Materials characterization
The X-ray diffraction was carried out using a Bruker D8 Discover diffractometer with Co-Kα radiation (Yokohama, Japan, λ = 1.7902 Å) at a scan rate of 0.5°per min. The microstructure and chemical composition were explored by a field-emission scanning electron microscope (Ultra 55, ZEISS, Oberkochen, Germany) coupled with an energy dispersive X-ray spectrometer (Quantax, Bruker, Billerica, MA, USA). The sample after LMD for cross-section imaging was prepared by mechanical polishing and ion milling (E-3500, Hitachi, Tokyo, Japan). Further investigations of the microstructure and chemical compositions were performed using a field-emission transmission electron microscope (JEOL JEM-2100F, 200 keV) with double spherical aberration correctors for both the probe-forming and image-forming objective lenses. Surface compositions of the samples were characterized by an X-ray photoelectron spectroscopy (XPS, AXIS ultra DLD, Shimazu) in a vacuum pressure of 10 −7 Pa with an Al Kα (mono) anode. The specific surface area was measured by N 2 adsorption-desorption method using BELSORP-mini II (BEL. JAPAN. INC) at 77.0 K.

Electrochemical characterization
All the electrochemical measurements were performed in 1.0 M KOH aqueous solution at 293 K using a Bio-Logic VSP 300 electrochemical workstation and a three-electrode electrochemical cell with a Pt wire or graphite rod counter electrode and an Ag/AgCl reference electrode. The powder samples were prepared from as-dealloyed sheet samples using a combination of mechanical grinding with a mortar and pestle and high-power ultrasonication at 130 W. 10 mg of nanoporous sample powder, 2 mg of conductive acetylene black (MTI Corp.), and 50 μL of Nafion solution (Wako Corp., 5 wt%) were dispersed in 1 mL of ethanol and sonicated for one hour to obtain a homogeneous ink. 39.2 μL of the ink was then cast onto a glassy carbon disk electrode (5 mm in diameter). The benchmark Pt/C catalyst was prepared from commercial Pt/ C (20 wt%) using the same mixture composition. The catalyst loading of the nanoporous catalysts and Pt/C was 2 mg cm −2 . A pure carbon electrode with a carbon loading of 0.4 mg cm −2 (equivalent to the loading of carbon components in the mixture electrodes) was also made by the same procedure without adding the nanoporous catalysts. For electrochemical measurements employing self-supported sheet samples, the sheet electrodes had a size of 1 cm × 0.5 cm × 170 μm. The high-load Pt/C catalyst was prepared by casting commercial Pt/C powders on a carbon paper. A total of 610 μL of the ink made by mixing 10 mg of Pt/C (20 wt%) and 125 μL of Nafion solution (5 wt%) in 1 mL of ethanol was drop-cast onto the carbon paper at a loading amount of 24.4 mg cm −2 and dried at room temperature. The polarization curves were characterized by cyclic voltammetry (CV) with a scan rate of 2 mV s −1 . iRcompensation was applied to all polarization curves based on resistance data measured by EIS at −0.9 V vs Ag/AgCl. The potential versus Ag/AgCl was changed into RHE based on E vs RHE = E vs Ag/AgCl + E Ø Ag/AgCl + 0.059 pH. The electrochemical impedance spectroscopy (EIS) was carried out at −0.2 V vs RHE with the frequency from 10 5 Hz to 0.01 Hz. The accelerated cyclic voltammetry cycling test was conducted at the scan rate of 50 mV s −1 for 5000 cycles. The chronoamperometric responses were tested by holding the potential at −0.15 V vs RHE. The double-layer capacitance (C dl ) was measured by CV in non-Faradaic potential region (−0.9 V to −1.0 V vs Ag/AgCl) with scan rates of 10, 20, 30, 40 and 50 mV s −1 . The electrochemical surface area (ECSA) is calculated by subtracting the capacitive contributions from carbon: where C dl is equivalent to the linear slope in the function of charging current density differences (Δj = |j a -j c | /2) and scan rate and C s is the specific capacitance with a moderate value of 0.040 mF cm −2 ECSA 10,72 .

Molecular dynamics simulation
Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) 73 was used to simulate the process of atom diffusion at the interfaces between Co (hcp), Mo (bcc), or Co 7 Mo 6 (intermetallic compound, μ-phase) and a magnesium. A 14 nm × 15 nm × 8 nm model